The English academy, or, A brief introduction to the seven liberal arts grammar, arithmetick, geometrie, musick, astronomie, rhetorick & logic : to which is added the necessary arts and mysteries of navigation, dyaling, surveying, mensuration, gauging & fortification, practically laid down in all their material points and particulars, highly approved to be known by the ingenious, and as such are desirous to profit, or render themselves accomplished : chiefly intended for the instruction of young scholars, who are acquainted with no other than their native language, but may also be very useful to other persons that have made some progress in the studies of the said arts / by John Newton.

CHAP. VI. Of the Rule of Fellowship.

THe Rules of plural proportion are those, by which we Resolved Questions that are discoverable by more Rules of Three than one, and cannot be performed by the double Rule of Three mentioned in the last chapter.

Of these Rules there are divers kinds and varieties, according to the nature of the Question propounded; I will only mention one, and refer the rest to my larger treatise of this Subject.

2. The Rule of plural proportion that I mean to mention, is the Rule of Fellowship.

3. And the Rule of Fellowship is that by which in Accompts amongst divers Men, (their several stocks together) the whole Loss or Gain being propounded, the Loss or Gain of each particular man may be disco∣vered.

4. The Rule of Fellowship is either single or double.

5. The Single Rule of Fellowship is, when the stocks propounded are single numbers; As in this Example: A and B were Partners in an Adventure to Sea, A put in 25. l. B 56, and upon return of the Ship, they sold the

Fraight for 50 l. profit; the question is, What part of this 50 l. is due to A, and what to B? to resolve this and the like Que∣stions, the sum of the stocks must be the first term in the Rule of Three, the whole gain the second, and each particular stock the third; this done repeating the Rule of Three, as often as there are particular stocks in the Question, the fourth term pro∣duced by these several operations are the respective Gains or Losses of those particu∣lar stocks propounded; so in the present question, the Resolution will be as here you see. 〈 math 〉〈 math 〉

6. The Double Rule of Fellowship is, when the stocks propounded are double numbers, that is, when each stock hath relation to a particular time. A, B, and C, hire a piece of Ground for 45 l. per Annum, in which A had 24 Oxen 32 days, B 12, for 48 days, C 16, for 24 days; now the question to be resolved is, What part of the Rent each person must pay?

For this purpose you must first Multiply each particular stock by its respective time, and take the total of their Products for the first term, the Gain or Loss for the second, and every man's particular stock and time

for the third; this done repeating the Rule of Three so often as there are Products of the double Numbers; the fourth terms pro∣duced upon those several operations are the numbers sought. So then in the question propounded, the Product of 24 and 32 is 768; the Product of 12 and 48 is 576, and the Product of 16 and 24 is 384, the sum of these Products is 1728, which is the first term, 45 l. the Rent is the second, and each particular Product the third; 〈 math 〉〈 math 〉

By which three Operations the question is Resolved.

FINIS.